Anonymous
Anonymous asked in Science & MathematicsMathematics · 1 decade ago

Find the value of this matrix?

1.[1 2 -1]

[3 -2 1]

[0 1 -3]

A. 26

B. 22

C. -16

D. 20

2. Find the inverse of

[3 1]

[-4 1]

thank you!!!

3 Answers

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  • Anonymous
    1 decade ago
    Favorite Answer

    1. The determinant of a 3x3 matrix in the form

    [a b c]

    [d e f]

    [g h i]

    is aei + bfg + cdh - afh - bdi - ceg.

    In your matrix, plugging in the variables gives:

    1*(-2)*(-3) + 2*1*0 + (-1)*3*1 - 1*1*1 - 2*3*(-3) - (-1)*(-2)*0

    = 6 + 0 + (-3) - 1 - (-18) - 0

    = 20

    2. If A is a n×n matrix, then take the augmented matrix [A | I_n] where I_n is the identity matrix of width n. After converting the left side of the augmented matrix to reduced row echelon form using elementary row operations, the right side is the inverse of A.

    [3 1 | 1 0]

    [-4 1 | 0 1]

    (1/3)r1 --> r1

    [1 1/3 | 1 0]

    [-4 1 | 0 1]

    4r1 + r2 --> r2

    [1 1/3 | 1/3 0]

    [0 7/3 | 4/3 1]

    (3/7)r2 --> r2

    [1 1/3 | 1/3 0]

    [0 1 | 4/7 3/7]

    (-1/3)r2 + r1 --> r1

    [1 0 | 1/7 -1/7]

    [0 1 | 4/7 3/7]

    Now that the left side is in row reduced echelon form, we know that the right side is the inverse.

    [1/7 -1/7]

    [4/7 3/7]

  • nle
    Lv 7
    1 decade ago

    1) expand to find determinant

    D. 20

    2) [ 1/7 -1/7 ]

    [4/7 3/7 ]

  • ?
    Lv 4
    3 years ago

    at the beginning your matrix isn't sq. with the aid of fact of this it would not signify a very defined gadget of linear self reliant equations. Secondly matrices don't have "zeros", applications have zeros. you desire something of the variety [A][x] = [b] [x] = inv(A) * [b] Use the matlab function inv(A) to locate the inverse. yet A might desire to be sq.. the extra suitable the matrix, the longer that is going to take for matlab to locate its inverse. If that is an exceedingly super matrix, attempt utilizing LU decomposition or guassian removing, particularly of direct inversion.

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